Learning control algorithms for tracking "slowly" varying trajectories

Abstract

To date, most of the available results in learning control have been utilized in applications where a robot is required to execute the same motion over and over again, with a certain periodicity. This is due to the requirement that all learning algorithms assume that a desired output is given a priori over the time duration t in [0,T]. For applications where the desired outputs are assumed to change "slowly", we present a D-type, PD-type, and PID-type learning algorithms. At each iteration we assume that the system outputs and desired trajectories are contaminated with measurement noise, the system state contains disturbances, and errors are present during reinitialization. These algorithms are shown to be robust and convergent under certain conditions. In theory, the uniform convergence of learning algorithms is achieved as the number of iterations tends to infinity. However, in practice we desire to stop the process after a minimum number of iterations such that the trajectory errors are less than a desired tolerance bound. We present a methodology which is devoted to alleviate the difficulty of determining a priori the controller parameters such that the speed of convergence is improved. In particular, for systems with the property that the product matrix of the input and output coupling matrices, CB, is not full rank. Numerical examples are given to illustrate the results.

A survey on iterative learning control for nonlinear systems

“…In Saab, Vogt, and Mickle (1997), a slowly iteration-varying tracking problem is considered, in which r iþ1 (t) ¼ r i (t) þ i (t) and the magnitude of i (t) is uniformly bounded by a small bound. It turns out that the ILC tracking error depends on the bound.…”

Iterative learning controllers with time-varying gains for large-scale industrial processes to track trajectories with different magnitudes

“…Meanwhile, for iterationdependent tracking, Moore's Group (Chen and Moore 2003) has addressed an adaptive feedforward compensation-based ILC to eliminate known iteration-wise sinusoidal disturbance to the measured output, which is still the unique desired trajectory tracking scheme without the convergence analysis. Besides, Saab et al (1997) has studied the problem of tracking slowly-varying trajectories each of which differs from the previous one within a small fluctuation level. In the latter study, only some bounded tracking error is guaranteed in the sense of Lambda-norm under the assumption that the non-repetitive desired trajectories are to be realisable and some disturbances are present.…”

Varying-order iterative learning control against perturbed initial conditions

“…In [4], a specific training method called selective learning was suggested to adjust the bias term, and the robustness of such a P-type learning algorithm was established. This kind of learning control has been applied to solve different tracking problems [6,7]. It should be noted that all the aforementioned are synthesized without applying optimization.…”